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2019 Moduli of stable maps in genus one and logarithmic geometry, II
Dhruv Ranganathan, Keli Santos-Parker, Jonathan Wise
Algebra Number Theory 13(8): 1765-1805 (2019). DOI: 10.2140/ant.2019.13.1765

Abstract

This is the second in a pair of papers developing a framework to apply logarithmic methods in the study of stable maps and singular curves of genus 1. This volume focuses on logarithmic Gromov–Witten theory and tropical geometry. We construct a logarithmically nonsingular and proper moduli space of genus 1 curves mapping to any toric variety. The space is a birational modification of the principal component of the Abramovich–Chen–Gross–Siebert space of logarithmic stable maps and produces logarithmic analogues of Vakil and Zinger’s genus one reduced Gromov–Witten theory. We describe the nonarchimedean analytic skeleton of this moduli space and, as a consequence, obtain a full resolution to the tropical realizability problem in genus 1.

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Dhruv Ranganathan. Keli Santos-Parker. Jonathan Wise. "Moduli of stable maps in genus one and logarithmic geometry, II." Algebra Number Theory 13 (8) 1765 - 1805, 2019. https://doi.org/10.2140/ant.2019.13.1765

Information

Received: 1 September 2017; Revised: 11 May 2019; Accepted: 4 July 2019; Published: 2019
First available in Project Euclid: 29 October 2019

zbMATH: 07118652
MathSciNet: MR4017534
Digital Object Identifier: 10.2140/ant.2019.13.1765

Subjects:
Primary: 14N35
Secondary: 14T05

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.13 • No. 8 • 2019
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